Holographic timelike entanglement and $c$ theorem for supersymmetric QFTs in ($ 0+1 $)d

TL;DR

This paper introduces a holographic approach to compute timelike entanglement entropy in supersymmetric quantum mechanical models, revealing its role as a measure of degrees of freedom and its connection to a $c$-theorem during RG flows.

Contribution

It develops a holographic framework for timelike entanglement entropy in ($0+1$)d SUSY QFTs and demonstrates its relation to RG flow and degrees of freedom.

Findings

tEE behaves like a holographic $c$-function during RG flow.

tEE correlates with complexity, indicating degrees of freedom.

Models show consistent behavior of tEE and complexity from UV to IR.

Abstract

We present a holographic set up that computes timelike Entanglement Entropy (tEE) in $ (0+1) $d QFTs preserving some amount of SUSY. The first example we consider is that of $\mathcal{N}=2$ matrix models with massive deformations. These are dual to non-Abelian T-dual of $AdS_5 \times S^5$ that asymptotes to \emph{smeared} D0 branes. The second example, that we consider is of $ \mathcal{N}=4 $ superconformal quantum mechanical quivers in ($ 0+1 $)d that are dual to a class of type IIB backgrounds with an $ AdS_2 $ factor. In both of these examples, tEE reveals a remarkable similarity with holographic $ c $ function pertaining to a RG flow. We further compute the complexity in these models, which also reveals an identical behaviour indicating the fact that tEE is a measure of number of degrees of freedom for these ($ 0+1 $)d SQFTs in a RG flow from UV to deep IR.